一种用图挖掘技术将社会图表示为多层图的方法(IJEME-V9-N1-3)

I.J.EducationandManagementEngineering,2019,1,20-36PublishedOnlineJanuary2019inMECS()DOI:10.5815/ijeme.2019.01.03Availableonlineat*Asst.Professor,DepartmentofCSE&A,IGIT,Sarang,Dhenkanal-759146,IndiaReceived:10July2018;Accepted:16October2018;Published:08January2019AbstractInSocialGraph,asetofentitiesornodesorverticesinteractwitheachotherinacomplicatedmannerthatcanformmultipletypesofrelationshipsthatdependontimeandtypesofcomplications.Suchgraphsincludemultiplesubsystemsandlayersofconnectivity.Soitisimportanttotakesuchmulti-layerfeaturesintoaccounttomakeeasierofunderstandingofsuchcomplexsystems.Inthispaper,theauthorfocusesonaSocialGraphtorepresentinamulti-layergraphbasedonitscharacteristicsliesineachnodeorvertexorentity.Forthis,theauthorproposesageneralmodelrelatedtoSocialGraph.Forthismodel,theauthorproposesanalgorithm,SoGraMforrepresentationofSocialGraphwithmulti-layerfeaturesusingGraphMiningTechniques.Further,theauthortriestoprovetheproposedalgorithmwiththreeexamplesofSocialGraphnamelyAuthorGraph,EmailGraph,andTelephoneGraph.IndexTerms:AdjacencyMatrix,Base-Layer,Multi-LayerGraph,SocialGraph,Sub-Layer.©2019PublishedbyMECSPublisher.Selectionand/orpeerreviewunderresponsibilityoftheResearchAssociationofModernEducationandComputerScience.1.IntroductionMulti-layernetworksexistwhenthereismorethanonesourceofconnectivityinformationforagroupofusers.Inthecontextofthesocialnetwork,thecommunicationlinkbetweentheusersisrelationalinformation.Sothereisapossibilityofderivingbehavioralrelationshipsbasedonuseractionsorinterests[9].Insocialnetworks,edgesarecategorizedbasedonthenatureoftherelationshipsoractionsthattheyrepresentareproposedby[6,13].Inthesocialnetworks,theedgeiscategorizedbyitstypearecalledmultiplexnetworksby[4]ormulti-relationalnetworksproposedby[6].Inthecomputerscienceandcomputationallinear-algebracommunities,tensor-decompositionmethodsproposedby[3,5]andmulti-waydataanalysisby*Correspondingauthor:E-mailaddress:AnApproachtoRepresentSocialGraphasMulti-LayerGraphUsingGraphMiningTechniques21[1]wereusedtostudyvarioustypesofmulti-layernetworks.Thesetypesofmethodsarebasedonrepresentingmulti-layernetworksasadjacencytensorsoforderhigherthantwo.Networkedsystemsthatcannotberepresentedastraditionalgraphswerestudiedfromadataminingpointofview.Heterogeneous(information)networksweredevelopedasageneralframeworktotakeintoaccountmultipletypesofnodesandedgescanbeseenin[2,12,14].Amultiplelayersofasocialnetworkwhichperformtaskssuchasinference,clustering,andanomalydetectionproposedby[7].Oftensocialnetworksincludedifferenttypesofnodesi.e.malesandfemalesorhierarchicalstructuresi.e.individualsareconsideredasorganizations,werestudiedusingmulti-levelnetworks,multiplelayers,andnetworksofnetworksby[4].Theextractionofinformationfromalargemulti-layersocialnetworkisproposedby[8].Amulti-layersocialnetworkmodelwhichcombinesallthedetectedsocialnetworkwhileencounterswithothersocialnetworksareproposedby[11].Thesemulti-layersocialnetworksareinvestigatedthroughrelationship.Asocialnetworkisdefinedasacomplexgraph,andeachunitisanindividual,village,household,country,etc.SothesocialnetworkmaybedefinedassetnodesorverticesV={V1,V2,…..,Vn}andbetweenthenodesorverticesthereisasetoflinksorconnectivityoredgesE={E1,E2,….,En}proposedby[9].Inthispaper,theauthorproposesanalgorithmwhichrepresentsasocialgraphasamulti-layergraphusinggraphminingtechniques.Forthis,theauthorsrepresentthreetypesofsocialgraphexamplesnamelyAuthorsGraph,EmailGraph,andTelephoneGraphthatconsistofmulti-layergraphswherethebase-layerorprincipallayerincludedifferenttypeofinteractionsbetweenentitiesornodesorvertices.Analgorithmwhichrepresentstelephonecalldurationgraphasamulti-layergraphisproposedby[10].Basedon[10]’salgorithm,theauthorproposesageneralalgorithmforrepresentationofthesocialgraphasamulti-layergraphhavingeachlevelisassociatedwithaparticularcharacteristic.2.Multi-layerNetworkIntherealworld,morethanonekindofconnectionscanexistbetweenanypairofindividuals.Asamatteroffact,forthistypeofsocialnetworks,itcanbetermedasthemulti-layernetwork,multi-relationalnetwork,multidimensionalnetwork,andmultiplexnetwork.AsocialnetworklayerLisaweightedgraphG(V,E)withvertexsetVcorrespondingtousersonthesocialnetworkandedgesetEVXVcorrespondingtosociallinksbetweenusers.Amulti-layersocialnetworkMLSN=(L1,L2,…….,Ln)isatuplewhereLi=Gi(V,Ei),i1,2,.…..,naresocialnetworklayers.Amulti-layernetworkG=(V,E)consistsofverticesV={V1,.......,Vn},commontoalllayers,andedgesE=(E1,.......,Em)inmlayers,whereEkistheedgesetforlayerk,andEk={𝑒𝑣𝑘;Vi,Vj∈V}.Eachedgeisconsideredasdirectedorundirecteddependingonitscharacteristics.Thedefinitionofmulti-layernetworkcanbeseenin[8].3.ProposedAlgorithmforRepresentationofSocialGraphasMulti-layerGraphTheproposedalgorithm,SoGraMhasonlyoneprocedurecalledShow(MLAM).Thealgorithmreadsthedatafromthedatasetfilecalled“Node_Dataset.Txt”whichcomprisesanumberoflayers,totaln